The stepping-stone method introduced by [1]}
is similar to PS in that it also uses samples from power posteriors, but the
idea is not based on approximating the integral per se, but by
the fact that we can accurately use importance sampling to approximate the
ratio of normalizing constants with respect to two pre-chosen
consecutive \(\beta \)  values at each step between the posterior and prior.
Also, [1]} chose the values of \(\beta \)  for the
series of power posteriors from which to sample so that most were close to
the prior (reference) distribution, rather than evenly distributed between
0 and 1.
This is beneficial, because most of the change happens near the prior; the
likelihood begins to dominate quickly, even at small values of \(\beta \) .
The stepping-stone method results in more accurate estimates of the marginal
likelihood with fewer steps than PS [1]}.
